There is a growing need for an in situ measurement of fluid properties and conditions. Historically such measurements were made using discretely-sampled, laboratory-based instruments or using manual gauges under a periodic maintenance schedule. In many industrial and commercial applications, the value of continuous process monitoring and process control are driving the development of new sensor technologies that can bring a reasonable subset of the laboratory instruments' capabilities directly into the process control and monitoring systems. In particular, there exists a need for a precision sensor to measure the viscosity of liquids and to perform other physical and chemical measurements within a liquid environment. Such a sensor should have little interference from other fluid properties.
Piezoelectric crystal sensors—and, in particular, thickness shear mode (TSM) resonators, while operated as sensors—have been shown to be promising candidates for such applications. The piezoelectric sensor offers a transduction mechanism between the physical loading of a mechanical structure and the electrical properties observed at one or more electrical ports.
The descriptions and specifications herein will be made clearer through the definition of several terms. Those terms not specifically defined below should be construed to conform to industry standard definition with primary reliance on the 1987 IEEE Standards on Piezoelectricity, ANSI/IEEE Std 176-1987, (The IEEE Standard hereinafter).
‘Mirror Surface’ or ‘Acoustic Mirror Surface’: a surface being an ideal plane surface, an ideal contoured surface (spherical or linear bevel), or having local deviations from an ideal plane surface or ideal contoured surface that are small compared to the acoustic wavelength. In these specifications, “small deviations” should be smaller than about 2% of a wavelength. The surface may define a boundary between the resonant acoustic wave device (AWD) and any other medium having a poor acoustic impedance match (such as water, air, vacuum, polymer, oil and the like, by way of example) giving rise to an acoustic reflection coefficient.
In the case of contoured surfaces, the surface is locally planar with a curvature, typically tailored to create an essentially spherical mirror with a defined focal length. Structures with textured surfaces, such as those provided by way of example in US patent application publication No. 2007-0144240 to Andle (which is incorporated herein by reference in its entirety) also fall within the scope of the term mirror surfaces provided that the textures represent deviations of less that 2% of the wavelength.
‘Mechanical planar structure’ or ‘planar structure’: A structure having at least two opposing ‘acoustic mirror surfaces’, said surfaces being functionally parallel surfaces, thereby allowing substantially collinear reflection of a wave therebetween, and having lateral extents at least four times its thickness. Classic examples include plano-plano resonators, plano-convex resonators, bi-convex resonators and the like. Planar structures may be embedded within a larger structure. A contoured structure falls within the present definition of a planar structure provided that the lateral dimensions of the structure are at least four times the maximum thickness.
By way of example, an inverted mesa is a planar structure etched into a larger substrate which is substantially inactive to the resonant mode of the planar structure. Further, multilayered structures, composite structures, and structures comprising composite materials offering homogeneous acoustic properties at the dimensional scale of the acoustic wavelength at least in the lateral direction are explicitly included within the term planar structures.
‘Trapped energy resonators’: a resonator which comprises a mechanical planar structure having a piezoelectric region, and in which the acoustic energy is substantially confined between the two faces of said structure and substantially confined laterally within the region defined by either contouring of the planar structure thickness or by mass loading and/or piezoelectric shorting associated with an optional transducer structure. The article “An Analysis of SC-Cut Quartz Trapped Energy Resonators with Rectangular Electrodes”, D. S. Stevens and H. F. Tiersten, 35th Annual IEEE Frequency Control Symp., pp. 205-212 (1981) discloses some typical examples of such trapped energy resonators.
Symmetry groups' (equivalently referred to as ‘Point groups’) are defined in the IEEE Standards on Piezoelectricity based on the rules of symmetry of repeating structure with respect to a point. The field of crystallography allows for seven crystal systems related to unit cells consisting of parallelepipeds having sides defining natural axes a, b, and c. Directions are defined in an ‘inverse space’ related to these coordinates. “As referred to the set of rectangular axes X, Y, Z, these indices are in general irrational except for cubic crystals. Depending on their degrees of symmetry, crystals are commonly classified into seven systems: triclinic (the least symmetrical), monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. The seven systems, in turn, are divided into point groups (classes) according to their symmetry with respect to a point. There are 32 such classes, eleven of which contain enantiomorphous (right and left handed) forms. Twelve classes are of too high a degree of symmetry to show piezoelectric properties. Thus twenty classes can be piezoelectric. Every system contains at least one piezoelectric class. A convenient summary of the 32 classes with examples is given in Table 3 of the IEEE standard.”
The IEEE Standard goes on to define the various symmetry groups and the assignment of mineral (a, b, c) to rectangular (X, Y, Z) Cartesian coordinates. The relationship between orientation and rotation is further stated. “To characterize a piezoelectric crystal, a set of piezoelectric constants is needed; and in order to make them unambiguous, a sign convention is necessary for both the constants and the axis sense. A specific relation between the a, b, c axes of crystallography and the X, Y, Z axes is given in 3.2.1-3.2.6, and summarized in Table 3 (of the IEEE Standard). The reader is cautioned at this point that, without general agreement on sign conventions, there can be much confusion. Data expressed in terms of one abc-XYZ relation look very different from the same data in terms of another abc-XYZ relation. In this IEEE Standard, the positive senses of the XYZ axes are defined such that certain piezoelectric constants are positive. Details for determining senses of the XYZ axes are described in 3.5. The choice of the positive sense is arbitrary in some cases. A discussion of static measurements related to sign determination will be found in 6.3.” The IEEE Standard goes on to show examples of rotated coordinates and the associated material properties. Throughout this document, it is assumed that the coordinate system is for unrotated ZX plates unless explicitly shown and/or described otherwise (such as done in relation to FIGS. 1 and 2). The IEEE standard strictly applies only to crystals, having translational symmetry (a repeating unit cell) and rotational symmetry (point groups); however common materials are not always single crystals and there exist polycrystalline materials and oriented polymers having piezoelectric properties. The general literature contemplates such materials that are aggregates, as well as other non-crystalline materials that are not considered by the IEEE Standard. The present application also refers to symmetry group ∞2. The infinite symmetry operator indicates isotropic properties around the primary axis. For example, a polycrystalline material with the c-axis oriented along Z but with random rotation of the individual crystal domains about their c axis will appear to be isotropic in the lateral directions and have infinite symmetry.
‘Shear mode’: a displacement vector field, {right arrow over (u)}, such that the magnitude of u is constant along any given closed field lines (mathematically ∇·{right arrow over (u)}=0) and vary between adjacent, substantially parallel, field lines (mathematically ∇×{right arrow over (u)}≠0).
‘Thickness shear mode’: an acoustic displacement vector field substantially parallel to the surface, having its primary change in magnitude along the axis substantially perpendicular to the surface.
‘Face shear mode’: an acoustic displacement vector field substantially parallel to the surface, having its primary change in magnitude along an axis lying substantially in the plane of the surface.
‘Radial shear mode’: a face shear mode in which the acoustic displacement vector field has significantly angular motion and the primary change in magnitude is substantially along the radius.
‘Lateral field excitation (LFE)’: the common term, referred to as lateral excitation in the IEEE Standard. LFE refers to the piezoelectric coupling between a lateral electric field component and acoustic stresses or strains within the structure. In these specifications, LFE shall relate to excitation intended to excite shear modes of vibration in light of the specific emphasis of improved LFE of shear mode resonators.
‘LFE excitation supporting material’ shall be defined as a material, composite material, structure, or composite structure such that, if the thickness direction is defined to be X3 (Cartesian Z), then the aggregate piezoelectric properties provide non-trivial values for one or more of the shear coupling constants, e14, e15, e16, e24, e25, and e24.
‘Thickness field excitation (TFE)’: TFE refers to the piezoelectric coupling between a perpendicular electric field component and acoustic stresses or strains within the structure. In the present specifications, TFE represents an undesired excitation and will be intended to include the ability to excite any modes of vibration using a thickness-aligned electric field.
‘TFE excitation supporting material’ shall be defined as a material, composite material, structure, or composite structure such that, if the thickness direction is defined to be X3 (Cartesian Z), then the aggregate piezoelectric properties provide non-trivial values for one or more of the shear coupling constants, e31, e32, e33, e34, e35, and e36.
‘Effective Thickness Inactive Piezoelectric (ETIP)’: a material, composite material, structure, or composite structure such that, if the thickness direction is defined to be X3 (Cartesian Z), then the aggregate piezoelectric properties provide a trivial value for the sum of the squares of the six piezoelectric constants, e3J, compared to the sum of the squares of the remaining shear coupling constants, e14, e15, e16, e24, e25, and e24.
‘Circularly polarized (CP)’: a curvilinear polarization of displacement vector, u, such that the field lines form non-crossing, closed loops. By way of example, FIG. 4a illustrates a simple circular polarization but the similarly, square, ellipsoid, triangular, and many other shapes fall under the definition, due to the functional definition of the field lines formed by such polarization.
‘Quadrature symmetry piezoelectric (QSP)’: a material, composite material, structure, or composite structure such that, if the thickness direction is defined to be X3 (Cartesian Z), then the aggregate piezoelectric properties approximately or fully satisfy either or both ofe25˜−e14≠0 and e15˜e24˜0ore26˜−e16.Most preferably only one condition is met and the remaining piezoelectric constants are zero.
‘Effective shear decoupled substrate (ESDS)’: a material, composite material, structure, or composite structure such that, if the thickness direction is defined to be X3 (Cartesian Z), then the aggregate elastic properties provide for trivial values for the matrix elements C14, C15, C16, C24, C25, C26, C34, C35, C36, and their transpose values. An ESDS offers little or no acoustic coupling between extensional modes and shear modes.
‘Effective pure shear substrate (EPSS)’: an ESDS that further provides for trivial values for the matrix elements C46, C56, and their transpose values. An EPSS offers little or no acoustic decoupling between circularly polarized shear modes and other spurious modes.
‘Coplanar circularly polarized transducer (CCPT)’: a plurality of electrodes formed on a common surface (planar or curvilinear) such that one or more electrode forms an functionally closed shape, said plurality of electrodes forming a plurality of shapes, each of said shapes being fully enclosed by, or fully enclosing, another shape and defining a gap therebetween. The electrodes therein are defined as coplanar circularly polarized electrodes (CCPE) and a CCPT comprises a plurality of coplanar circularly polarized electrodes separated by at least one gap therebetween.
‘Functionally closed shape’ implies that small gap or gaps in the shape may be introduced that, while geometrically breaking the closed shape, will have minimal effect on the circular polarization induced by the CCPT. By way of example, such gap or gaps may be utilized for connecting metal to an enclosed electrode. FIGS. 6, 8, 9, and 10 show the simplest case of concentric coplanar electrodes being two-terminal, single port transducer structures. FIG. 11 illustrates some more complex cases incorporating three-terminal, two-port structures offering isolated input and output ports. The figure also illustrates that the incorporation of interconnecting metal between said closed shapes or through small breaks in said shapes is explicitly contemplated.
‘Circularly polarized LFE (CP-LFE)’: broadly defined as a nontrivial piezoelectric coupling between a circularly polarized acoustic displacement field and an applied potential via the lateral field components of the electric fields associated with said potential.
‘Functionally Z-cut’: a material, composite material, structure, or composite structure such that, if the thickness direction is defined to be X3 (Cartesian Z), then the aggregate elastic and piezoelectric properties of said material, composite material, structure, or composite structure, if measured, would closely be described by constants substantially unrotated from Z-cut as given in the IEEE Standard.
Throughout the definitions and the discussion that follows it is implicit that the piezoelectric effect is reciprocal and that if an electric field can excite an acoustic field, then said acoustic field can conversely excite the corresponding electric field. Teachings in which an electric potential is applied and a resonance is excited implicitly incorporate the converse.
Prior art FIG. 1 illustrates a simplified cross section of a quasi-parallel plate TSM resonator in which the acoustic displacements are confined between two nominally mirror surfaces 109a and 109b. TSM resonators are widely employed in frequency control and in sensor applications since the energy efficiency remains good with air loading and even with fluid loading. Other acoustic modes tend to couple energy into the bounding medium unless the boundaries are maintained in vacuum. The acoustic vibration is polarized parallel to the surfaces along X and the amplitude of said vibrations varies with thickness along Z. The example in FIG. 1 uses thickness field excitation (TFE) wherein the electric field is polarized parallel to the thickness of the crystal. Cartesian coordinates are shown typical of a simple ZX plate as defined in the IEEE Standard. Rotation of the crystallographic axes is typically required to obtain desirable properties and is assumed implicitly. The top surface 109a supports a common electrode 102. The lower surface 109b supports active input 103 and output 104 electrodes that respectively apply and sense electric vector fields with respect to the common electrode 102. The figure illustrates the electric vector fields of the driven 107 and sensed 108 thickness field excitation (TFE) resonators and the associated trapped energy acoustic displacements 105 and 106. The relative polarity corresponds to the known symmetric mode of the coupled resonator, monolithic crystal filter (MCF).
The overwhelming majority of the prior art employs planar surface, parallel plate (colloquially known as plano-plano) resonators. For illustrative purposes, the piezoelectric element 101 in FIGS. 1 and 2 is not drawn to scale and the curvature of the mirror surfaces 109a and 109b is exaggerated, to illustrate more clearly the breadth of the concept disclosed herein and its applicability to a wide variety of planar structures. Despite the graphical exaggeration, the figures are meant to depict a width exceeding four times the thickness.
The idealized TFE structure has a Z-variation of an X displacement, being stress and strain component 5 in the IEEE Standard. The Z material would support TFE of the desired mode only if the rotated piezoelectric constant, e35, is non-trivial. Rotating around the X axis such that crystallographic Y was normal to the surface would attain this result in quartz.
An alternate prior art sensor geometry is illustrated in FIG. 2, which depicts a resonator sensor using lateral field excitation (LFE). A lateral electric vector field 111 applied between electrodes 103 and 104 is parallel to X and excites a thickness shear acoustic displacement field 110 parallel to Y with variation along Z. Electrode 102 is optional in this case and serves no role in the desired lateral field excitation (LFE) of the structure.
The stress/strain component is 4 according to the IEEE Standards. The Z material would support LFE of the desired mode only if the rotated piezoelectric constant, e14, is non-trivial.
It will be clear to the skilled in the art that inclusion of an upper electrode 102 in proximity to the LFE electrodes 103 and 104 will introduce both TFE excitation and LFE excitation causing measurement difficulties and/or errors.
The coupling strength of a wave coupled to a piezoelectric device is typically approximated as
      k    2    =            e      2              ɛ      ⁢              C        _            where e is the effective piezoelectric constant (e14 for LFE and e35 for TFE), ∈ is the appropriate dielectric constant, and C is the effective elastic constant. For LFE in a Y-cut crystal as depicted in FIG. 2, C equals approximately (1+k2LFE)C44 while for TFE it is approximately (1+k2TFE)C55. A preferred embodiment for a LFE device would have k2LFE>>k2TFE, requiring the rotated constants to provide e14>>e35. Quartz and LiNbO3 substrate orientations, presently employed in LFE sensor devices do not meet these requirements.
In addition to the thickness field piezoelectric coupling of FIG. 1 and the lateral field excitation shown in FIG. 2, excitation through one or more spiral antenna/transducer systems is also known. This approach does not provide exclusively LFE but rather applies both lateral and thickness fields. Furthermore, the radial fields excite radially-polarized thickness shear modes, not circularly polarized shear modes.
The purely shear displacement component of an acoustic wave cannot couple to an ideal liquid. There exists a slight perturbation from this ideal case for a viscous liquid. The viscously entrained liquid has laminar flow and alters both the resonant frequency and power loss (crystal resistance) of the piezoelectric resonator sensor. The sensor may also interact with adsorbed mass or stiffening viscoelastic films on the surface, as is well known in the art.
Presently, thickness shear mode is the most popular solution to fluid phase sensing using piezoelectric sensors. These sensors typically employ a linearly-polarized acoustic displacement substantially in the plane of the planar polished surface. Components of displacement perpendicular to the surface cannot be avoided in present designs and result in radiative losses of acoustic energy into the fluid. The precise measurement of certain physical and chemical parameters often makes minimization or elimination of such unrelated fluid interactions highly desirable.
In frequency control applications the resonator is not placed in contact with a liquid; however radiative losses into air can limit performance and, again, the perpendicular components of displacement are undesirable.
These undesirable radiative losses are inherent to finite geometry resonators. An ideal resonator, constrained in only the thickness dimension but of infinite lateral dimension, does not suffer from such loses, but is clearly impractical. Real resonators have finite lateral dimensions and exhibit energy distributions similar to those seen in FIG. 3. FIG. 3 assumes a Y-cut plate in accordance with a prior patent application from which it is reproduced. Introducing finite length, l, along X, illustrates the problem. The mode profile is shown with a wave displacement 301 for n=1 and j=1 as UX=AX sin(πY/t) cos(πX/l). In practice there is finite extension of the wave beyond the electrodes and j=J−δ. Also shown is the corresponding amplitude component 302, UY(X,Y)=(t/l)AX sin(πX/l)sin(πY/t) for j=1.
Introducing a finite dimension in X introduces a lateral variation to Ux that can be simplistically estimated as UX (X,Y,Z)=AX cos(jπX/l)sin(nπY/t)cos(mπZ/w) for a length, l, and width, w. The wave-vector gains an X component, Kx=jπ/l. In this case the shear wave condition of U·K=0 is no longer satisfied unless there is an additional acoustic amplitude, UY (X,Y,Z)=jt/nl AX sin(jπX/l)sin(nπY/t)cos(mπZ/w). Finite extent along the direction of vibration results in a vertical wave component and the pure shear solution is no longer tangentially polarized at the device's surface. This results in local vertical motion of the interface between the resonator and the surrounding medium and the associated radiation of energy, causing compressional waves to radiate into the surroundings. In practical devices this effect is minimized by selecting a pure shear horizontal substrate, making the mode number, j, small and employing electrodes with small thickness to length ratio (approximating infinite plane devices). As such, common wisdom teaches the use of large electrode area to minimize compressional wave radiation limited by the required frequency separation of additional anharmonic modes. While mitigating the effect, in some applications further improvement is still required.
While thickness shear modes are by far the most common planar structure, the variation of amplitude could occur along a direction in the surface plane but perpendicular to the direction of the acoustic vibration. This motion is known as face shear since the exposed face of the crystal is deformed in a shear motion. The analogous motion to face shear in cylindrical coordinates provides circular lines of motion with amplitudes that vary along the radius of a disk. Such a circularly polarized face shear mode is a radial shear mode.
The defining feature common to the state of the art is the induction by the structure, of acoustic displacement vector fields with primarily linear polarization that have divergence at one or more boundaries of the sensor's active area, as depicted in FIG. 3, taken from application U.S. Ser. No. 12/036,125 to Andle, titled “Sensor, system, and method, for measuring fluid properties using Multi-Mode Quasi-Shear-Horizontal Resonator”, which is incorporated herein by reference. The '125 disclosure analyzes the effects of divergence in linearly polarized quasi-shear wave resonators in further detail and presents methods through which to employ the non-shear components of said resonances. Specifically the '125 invention relies on the subtle differences in the interaction of two or more acoustic resonance states or waveguide modes of a multi-mode resonator or waveguide. The most preferred embodiment is a dual-mode coupled resonator filter geometry with one resonant mode having a high degree of symmetry and the other having a high degree of anti-symmetry. By combining the additional information of multi-mode operation with the inherent ability of a horizontally-polarized quasi-shear-horizontal acoustic wave device (AWD) to operate in fluid environments, one obtains a multi-mode quasi-shear-horizontal (MMQSH) resonator.
In contrast, the present invention seeks to minimize or eliminate these non-shear components to obtain a substantially pure shear mode resonance with substantially horizontal polarization. The pure shear wave has zero net divergence of the acoustic displacement vector field. Such divergent fields at the device boundary require a conversion of in-plane (horizontal) shear displacement into other out-of-plane displacements. This conversion invariably leads to surface motion normal (vertical) to the plate surface of the crystal, and an associated radiation of propagating wave energy into even an ideal liquid. Such radiation in turn leads to frequency shifts and radiative losses under fluid load that are independent of viscosity or that occur even in air. Such radiative loses reduce the measurement precision, especially of low viscosity fluids. The associated frequency shifts and losses are also independent of added mass, further reducing sensor reliability as a microbalance for the detection of small added masses. In frequency control applications the Q of the resonator and therefore the stability of the oscillator are impacted by even the compressional wave radiation into air.
There exists significant motivation to discover structures in which the divergence of the acoustic displacement fields truly is zero everywhere and which do not suffer competing mode excitation methods. A vector displacement field with zero divergence is solenoidal, i.e. it forms closed lines of field flux. In a planar device these acoustic displacement vector field lines are preferentially parallel to the surface with nominally circular lines of flux as schematically depicted in FIG. 4a. A top view of the substrate 401 depicts idealized lines of surface displacement counterclockwise 402 and clockwise 404 with a dashed line indicating the null of motion 403. The null of movement frequently occurs at the region of maximum shear strain (derivative of the rate of change of amplitude of adjacent lines of movement). The amplitude of the vector displacement field is equal at all points on a given closed line and there are thus no divergences of the vector field.
A mode having non-divergent flux lines of its vector field being substantially parallel to the surface of the substrate and substantially circular or elliptical in form, as depicted in the idealized case of FIG. 4a, shall be deemed “circularly polarized”. The angle of the lines of acoustic displacement vector field components with respect to the surface shall be within 10° to be considered substantially parallel, preferably within 5°, and most preferably within 1°. The prior art case of FIG. 4b depicts a side view of a substrate 407 having lines of displacement 405 representing the fields of a traditional TSM resonator. Near the points of divergence at the ends of the vectors there exists a vertical component of motion corresponding to an angle of the vector with respect to the surface of θ 406. Since the vectors are time harmonic, the angle is also time harmonic and θ is the magnitude. The ends of the vectors “flap” up and down, causing piston-like radiation of sound waves into the adjacent media. Only in the limiting case of small angles are these unwanted losses minimized.
A circularly polarized wave has lines of displacement that close upon themselves and therefore have neither a beginning nor an end, eliminating the problematic divergence as was seen in FIG. 4a. Since the magnitude of the displacement is substantially equal on any such loop, there is no conversion to plate-normal components. It should be noted that for anisotropic crystals the polarization is more elliptical than circular and for the purposes of this disclosure “circularly polarized” shall broadly include any mode representing a solution to the coupled wave equations and having a mode shape having substantially zero divergence. The patterns 402 and 404 represent one such arbitrary case and the actual patterns will be dictated by the crystal symmetry of the substrate 401 and the geometry of the transducer, which should be judiciously chosen to best match the substrate anisotropy.
There is a long felt, and as of yet unresolved need in the industry for a fluid/liquid property sensor that will overcome the disadvantage and inaccuracies of present sensors. Furthermore, there is a significant advantage for providing a mechanical planar structure which minimizes out-of-plan divergence in shear mode resonators for other applications such as frequency control, and the like.